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Graphon mean-field backward stochastic differential equations with jumps and associated dynamic risk measures

Author

Listed:
  • Hamed Amini

    (University of Florida)

  • Zhongyuan Cao

    (NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai)

  • Agnès Sulem

    (INRIA Paris)

Abstract

We study backward stochastic differential equations (BSDEs) with jumps with mean-field type heterogeneous interactions governed by graphons, and associated dynamic risk measures. We prove existence, uniqueness and measurability results of solutions of these systems under some regularity assumptions and provide moment estimates. Under additional conditions, comparison theorems are obtained. Continuity and stability of such systems are also established. We then prove convergence of finite interacting mean-field particle systems with heterogeneous interactions to graphon mean-field BSDEs. Finally, we introduce the graphon dynamic risk measure induced by the solution of a graphon mean-field BSDE system and study its properties. In particular, a dual representation theorem is provided in the convex case.

Suggested Citation

  • Hamed Amini & Zhongyuan Cao & Agnès Sulem, 2025. "Graphon mean-field backward stochastic differential equations with jumps and associated dynamic risk measures," Finance and Stochastics, Springer, vol. 29(4), pages 1139-1194, October.
    • Handle: RePEc:spr:finsto:v:29:y:2025:i:4:d:10.1007_s00780-025-00575-3
    DOI: 10.1007/s00780-025-00575-3
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    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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